Studying the Performance of the Jellyfish Search Optimiser for the Application of Projection Pursuit
Sep 4, 2024
Optimisation in projection pursuit
- Data: \(\mathbf{X}_{n \times p}\); Basis: \(\mathbf{A}_{p\times d}\)
- Projection: \(\mathbf{Y} = \mathbf{X} \cdot \mathbf{A}\)
- Index function: \(f: \mathbb{R}^{n \times d} \mapsto \mathbb{R}\)
- Optimisation: \(\arg \max_{\mathbf{A}} f(\mathbf{X} \cdot \mathbf{A}) ~~~ s.t. ~~~ \mathbf{A}^{\prime} \mathbf{A} = I_d\)
- 5 vars (\(x_1\) - \(x_5\)), 1000 obs simulated
- One variable (\(x_2\)) is a mixture normal
- others are random normal
- 1D projection using the holes index: \(\propto 1 -\frac{1}{n} \sum_{i = 1}^n \exp(-\frac{1}{2} y_i y_i^{\prime})\)
Continuation of the previous work
